[Maths Class Notes] on Factors of 25 Pdf for Exam

Factors of a number are the product of such numbers which completely divide the given number. Factors of a given number can be either positive or negative numbers. By multiplying the factors of a number we get the original number. For example 1, 2, 3, 6 are the factors of 6. On multiplying two or more numbers we get 6. Hence we have 2 x 3 = 6 or 1 x 6 = 6. On this page, we will study the factors of 25 definitions, what are the factors of 25, what is the prime factorization of 25, factor tree of 25, and examples. Factor pairs of the number 25 are the pairs of the whole numbers which could be either positive or negative but not a fraction or decimal number. Factorisation is the common method to find the factors of 25. Let us study the prime factorization of 25.

 

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Factors of 25 Definition

The factors of a number are defined as the numbers which when multiplied will give the original number, by multiplying the two factors we get the result as the original number. The factors can be either positive or negative integers.

 

Factors of 25 are all the integers that can evenly divide the given number 25.

Now let us study how to calculate all factors of 25.

 

What are the Factors of 25?

According to the definition of factors of 25, we know that factors of 25 are all the positive or negative integers which divide the number 25 completely. So let us simply divide the number 25 by every number which completely divides 25 in ascending order till 25.

 

25 ÷ 1 = 25

 

25 ÷ 2 = not divides completely

 

25 ÷ 3 = not divides completely

 

25 ÷ 4 = not divide completely

 

25 ÷ 5 = 5

 

25 ÷ 6 = not divides completely

 

Similar numbers from 7 to 24 does not divides 25

 

25 ÷ 25 = 1

 

 So all factors of 25: 1, 5, and 25.

 

 We know that factors also include negative integers hence we can also have, 

 

list of negative factors of 25: -1, -5, and -25.

 

All Factors of 25 can be Listed as Follows

 

 

Hence 25 have a total of 3 positive factors and 3 negative factors.

 

All Factor Pairs of 25

All Factor Pairs of 25 are combinations of two factors that when multiplied together give 25.

 

List of all the positive pair factors of 25

 

1 x 25 = 25; (1, 25)

 

5 x 5 = 25; (5, 5)

 

So (1, 25), and ( 5, 5), are the positive pair factors of 25

 

As we know that Factors of 25 include negative integers too. 

 

List of all the negative pair factors of 25:

-1 x -25 = 25

 

-5 x -5 = 25

 

So (-1, -25), and ( -5, -5) are the negative pair factors of 25

 

Now we will study what is the prime factorization of 25.

 

What is The Prime Factorization of 25

According to the prime factor definition, we know that the prime factor of a number is the product of all the factors that are prime( a number that divides by itself and only one). Hence we can list the prime factors from the list of factors of 25.

 

Or the other way to find the prime factorization of 25 is by prime factorization or by factor tree.

 

Now let us study prime factors of 25 by division method.

 

Prime Factors of 25 by Division Method

To calculate the prime factors of 25 by division method, first, take the least prime number that is 2. Divide it by 2 until it is completely divisible by 2. If at a point it is not divisible by 2 take the next least prime number that is 3. Perform the same steps and move forward, till we get 1, as the quotient. Here is the stepwise method to calculate the prime factors of 25

 

Step 1: Divide 25 with 2

 

25 ÷ 2 = 12.5

 

As it is not divisible by 2 completely let us take next prime number 3 

 

Step 2: Now divide 25 by 3

 

25 ÷ 3 = 8.33

 

It is also not divisible by 3. so let us check with other prime numbers. 

 

Step 3: Now 25 is  divisible by 5

25 ÷ 5 = 5

 

Step 4: Now 5 is again divisible by 5

5 ÷ 5 = 1

We get the quotient 1.

 

From the above steps, we get a prime factor of 25 as 5 x 5= 52

And also, common factors of 25 are 5 x 5

 

The number 25 is a composite number because 25 can be divided by 1, by itself, and by 5. 5 is a prime number so we cannot split it into more prime numbers, and hence the factor tree of 25 is incomplete. Here is the factor tree of 25.

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Solved Examples

Example 1: Write down the factors of 21.

Solution:

21 ÷ 1 = 21

21 ÷ 3 = 7

21 ÷ 7 = 3

21 ÷ 21 = 1

Therefore the factors of 16 are 1, 3, 7, and 21.

 

Example 2: Write down the factors of 71.

Solution:

71 ÷ 1 = 71

71 ÷ 71 = 1

71 is a prime number so it has only two factors 1 and the number itself. Therefore the factors of 71 are 1 and 71.

 

Quiz Time

1. Find the factors for 21

2. Find the factors for 46

 

Importance of Factors 

Factors are an important chapter in Maths. Everything around us in our daily lives has to do with factors. Telling the time or knowing the proportion of ingredients that are needed in order to bake a cake, are done via the knowledge of Factors. Knowing how to divide a number into equal parts is done through factors. You also need factors to compare the prices of products when you go to a store. All students of Maths need to have a sound understanding of the chapter on Factors. Questions that come from Factors can be quite scoring if the students learn about them well and practice on a regular basis.

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